基于贝叶斯方法的比例数据分位数推断及其应用
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摘要
为了尝试使用贝叶斯方法研究比例数据的分位数回归统计推断问题,首先基于Tobit模型给出了分位数回归建模方法,然后通过选取合适的先验分布得到了贝叶斯层次模型,进而给出了各参数的后验分布并用于Gibbs抽样。数值模拟分析验证了所提出的贝叶斯推断方法对于比例数据分析的有效性。最后,将贝叶斯方法应用于美国加州海洛因吸毒数据,在不同的分位数水平下揭示了吸毒频率的影响因素。
In this paper,we try to use Bayesian method to investigate the regression modeling of the proportional data in the framework of quantile regression.We first give the proposed quantile regression for proportional data based on Tobit model,and then obtain the Bayesian hierarchical model through choosing appropriate prior distributions,which lead to the posterior distribution for Gibbs sampling method.The usefulness and good performance of our proposed method is examined by the simulation studies.Finally,we apply newly proposed method to the heroin use data in California,and reveal the influence factors of drug use frequency at different quantile levels.
In this paper,we try to use Bayesian method to investigate the regression modeling of the proportional data in the framework of quantile regression.We first give the proposed quantile regression for proportional data based on Tobit model,and then obtain the Bayesian hierarchical model through choosing appropriate prior distributions,which lead to the posterior distribution for Gibbs sampling method.The usefulness and good performance of our proposed method is examined by the simulation studies.Finally,we apply newly proposed method to the heroin use data in California,and reveal the influence factors of drug use frequency at different quantile levels.
引文
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[5]Zhao W,Zhang R,Lv Y,Liu J.Variable Selection for Varying Dispersion Beta Regression Model[J].Journal of Applied Statistics,2014,41(1).
[6]Ramalho E,Ramalho J,Murteira J.Alternative Estimating and Testing Empirical Strategies for Fractional Regression Model[J].Journal Econometrics Survery,2011,25(1).
[7]李泽安,葛建芳,章亚娟.Beta回归模型在数据挖掘预测中的应用[J].南通大学学报:自然科学版,2009,8(3).
[8]赵为华,张日权.Beta-Binomial回归模型及其应用[J].统计与信息论坛,2016,31(3).
[9]Koenker,Roger Bassett,Gilbert.Regression Quantiles[J].Econometrica:Journal of the Econometric Society,1978(1).
[10]Koenker,Roger.Quantile Regression[M].Cambridge:Cambridge University Press,2005.
[11]Tobin J.Estimation of Relationships for Limited Dependent Variables[J].Econometrica,1958,26(1).
[12]Amemiya T.Tobit Models:A Survey[J].Journal of Econometics,1984,24(1).
[13]Rahim Alhamzawi,Keming Yu.Bayesian Tobit Quantile Regression Using G-prior Distribution with Ridge Parameter[J].Journal of Statistical Computation and Simulation,2015,85(14).
[14]Kaifeng Zhao,Heng Lian.Bayesian Tobit Quantile Regression with Single-index Models[J].Journal of Statistical Computation and Simulation,2015,85(6).
[15]Andrews D,Mallows C.Scale Mixtures of Normal Distributions[J].Journal of the Royal Statistical Society,1974,36(1).
(1)有需要了解的读者请与作者联系。
[2]Ferrari S,Cribari-Neto F.Beta Regression for Modelling Rates and Proportions[J].Journal of Applied Statistics,2004(7).
[3]Papke L,Wooldridge J.Econometric Methods for Fractional Response Variables with an Application to 401(k)Plan Participation Rates[J].Journal of Applied Econometrics,1996,11(6).
[4]Kieschnick R,McCullough B.Regression Analysis of Variates Observed on(0,1):Percentages,Proportions and Fractions[J].Statistical Modelling,2003(3).
[5]Zhao W,Zhang R,Lv Y,Liu J.Variable Selection for Varying Dispersion Beta Regression Model[J].Journal of Applied Statistics,2014,41(1).
[6]Ramalho E,Ramalho J,Murteira J.Alternative Estimating and Testing Empirical Strategies for Fractional Regression Model[J].Journal Econometrics Survery,2011,25(1).
[7]李泽安,葛建芳,章亚娟.Beta回归模型在数据挖掘预测中的应用[J].南通大学学报:自然科学版,2009,8(3).
[8]赵为华,张日权.Beta-Binomial回归模型及其应用[J].统计与信息论坛,2016,31(3).
[9]Koenker,Roger Bassett,Gilbert.Regression Quantiles[J].Econometrica:Journal of the Econometric Society,1978(1).
[10]Koenker,Roger.Quantile Regression[M].Cambridge:Cambridge University Press,2005.
[11]Tobin J.Estimation of Relationships for Limited Dependent Variables[J].Econometrica,1958,26(1).
[12]Amemiya T.Tobit Models:A Survey[J].Journal of Econometics,1984,24(1).
[13]Rahim Alhamzawi,Keming Yu.Bayesian Tobit Quantile Regression Using G-prior Distribution with Ridge Parameter[J].Journal of Statistical Computation and Simulation,2015,85(14).
[14]Kaifeng Zhao,Heng Lian.Bayesian Tobit Quantile Regression with Single-index Models[J].Journal of Statistical Computation and Simulation,2015,85(6).
[15]Andrews D,Mallows C.Scale Mixtures of Normal Distributions[J].Journal of the Royal Statistical Society,1974,36(1).
(1)有需要了解的读者请与作者联系。